Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator

被引：1

作者：

Korosteleva, D. M. ^{[1
]}

Solov'ev, S. I. ^{[2
]}

机构：

[1] Kazan State Power Engn Univ, Kazan 420066, Russia

[2] Kazan Fed Univ, Kazan 420008, Russia

来源：

UCHENYE ZAPISKI KAZANSKOGO UNIVERSITETA-SERIYA FIZIKO-MATEMATICHESKIE NAUKI | 2023年 / 165卷 / 02期

关键词：

eigenvibration; shallow shell; oscillator; eigenvalue; eigenvector; eigenvalue problem; finite element method; Hermite finite element;

D O I：

10.26907/2541-7746.2023.2.153-166

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The problem was approximated by the mesh scheme of the finite element method with Hermite finite elements. Theoretical error estimates for the approximate solutions were proved. The theoretical findings were verified by the results of numerical experiments.

引用

页码：153 / 166

页数：14

共 11 条

[1] Adams R. A., 1975, SOBOLEV SPACES
[2] Andreev L.V., 1988, Dynamics of Plates and Shells with Concentrated Masses
[3] Andreev L.V., 2012, Dinamika tonkostennykh konstruktsii s prisoedinennymi massami (Dynamics ofThin-Walled Constructions with Attached Masses)
[4] Brenner S.C., 1994, The Mathematical Theory of Finite Element Methods
[5] C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
Brenner, SC
Sung, LY
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2005, 22-3 (01) : 83 - 118
[6] Ciarlet P.G., 1978, CLASSICS APPL MATH, V4, P530, DOI [10.1137/1.9780898719208, DOI 10.1137/1.9780898719208]
[7] Litvinov V.G., 1987, Optimization in Elliptic Boundary Value Problems with Applications to Mechanics
[8] Mikhlin S.G., 1977, Linear Partial Differential Equations
[9] Seregin S.V., 2016, Dynamics of Thin Cylindrical Shells with Attached Mass
[10] Approximation of variational eigenvalue problems
Solov'ev, S. I.
[J]. DIFFERENTIAL EQUATIONS, 2010, 46 (07) : 1030 - 1041

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